I. Basic concepts: Buoyancy and Elasticity II. Estimating Tax Elasticity III. From Mechanical Projection to Forecast


 Clementine Jenkins
 3 years ago
 Views:
Transcription
1 Elements of Revenue Forecasting II: the Elasticity Approach and Projections of Revenue Components Fiscal Analysis and Forecasting Workshop Bangkok, Thailand June 16 27, 2014 Joshua Greene Consultant IMFTAOLAM training activities are supported by funding of the Government of Japan Lecture Outline I. Basic concepts: Buoyancy and Elasticity II. Estimating Tax Elasticity III. From Mechanical Projection to Forecast This training material is the property of the International Monetary Fund and is intended for the use in Institute for Capacity Development (ICD) and Fiscal Affairs Department (FAD) courses. Any reuse requires the permission of ICD and FAD. 1
2 I. Introduction and Basic Concepts The elasticity approach: one of the most commonly used conditional forecasting methods Like the effective tax rate approach, changes in tax revenue reflect mainly changes in the tax base if policy is unchanged What is different about the elasticity approach: Revenues can rise faster or more slowly than changes in tax base ( nonlinear response ) Forecast: combines mechanical projection with estimated impact of any tax change and judgment (to reflect possible variations in compliance or other information on specific shocks to tax collection). 3 Buoyancy Buoyancy of a tax is the realized/observed relative variation in revenue collection or a specific revenue item compared to the relative change in the proxy tax base: Buoyancy = ( T/ T) / ( Base/Base) Thus, buoyancy is based on actual revenues and reflects all changes in the tax system, including the tax rates and brackets, the definition of the base, variations in enforcement/compliance, or other specific shocks. A tax is said to be buoyant if the tax revenues increase more than proportionately to a rise in output. 4 2
3 Elasticity The elasticity of a tax measures the automatic response of tax revenue to changes in the tax base. Elasticity = ( AT/ AT) / ( TB/TB) The elasticity excludes the effects of discretionary changes in the tax structure (tax rates, coverage, exemptions, and deductions) or administration, as well as the introduction of new taxes. Thus, the elasticity can differ from the buoyancy (next slide) is based on adjusted, rather than actual, revenues The elasticity must be estimated by removing the effects of discretionary changes from revenue data. This can be hard to do (need estimates of effects of these changes). 5 Forecasts with Buoyancies and Elasticities lnr Ln(Actual Rev.) = a + b lnb  using estimated buoyancy Ln(Adjusted Rev.) = + lnb  using estimated elasticity lnb 6 3
4 Proportional Adjustment Method: An Example for Adjusting Revenue Year Actual Tax Discretionary Tax Collection Share of Adjusted d Collections Measure Excluding New Measure Tax Measure in Revenue Receipts T DS T  DS T/(TDS) T* Col Elasticity Golden rule: the tax system is such that elasticity of tax revenues to the tax base should ideally be close to 1. In practice, estimated elasticity can differ from 1. Progressive income taxes can have an elasticity > 1 Lagged indexation of tax brackets to inflation or wages raises elasticity. Proportional (advalorem) taxes (VAT, payroll tax) more likely to exhibit estimated elasticity of 1. Elasticity below 1 is possible for specific taxes (e.g., excise or stamp duties) if they are not indexed and/or collected promptly, or if consumers devote smaller shares of income to these items over time (e.g., tobacco products). 8 4
5 Elasticity Inflation can raise or lower the elasticity. Inflation can boost income tax elasticity if collection occurs shortly after assessment (progressivity and delayed indexation of brackets). Inflation will depress elasticity of all taxes if significant collections lags the real value of the tax dues is eroded (OliveiraTanzi effect), i.e., tax base is growing faster than revenues. For practical purposes: Any estimated elasticity very different from 1 (e.g., 0.5 or 2) should raise questions: can you explain it? More importantly: if you cannot estimate the elasticity (because data adjustment is hard), beware of highly unstable buoyancies from year to year 9 Elasticity The arithmetic of nonunitary elasticity. 0.3 Reven nue to tax base ratio unitelasticity 1.5 elasticity 2 elasticity 0.5 elasticity 10 5
6 Elasticity For mediumterm forecast: safe to assume that outeryear elasticities are unlikely to stay very high or very low. Tax brackets are ultimately indexed; Limits to gains from better tax administration (compliance and enforcement, ). Translating other basic forecasting techniques in terms of elasticity: Effective tax rate approach: Keeping ETR constant = unit elasticity Raising ETR: above 1 elasticity Simple extrapolations of tax revenue: Equivalent to unit elasticity if projected revenue growth is the same as the projected growth in the tax base 11 II. Estimating Tax Elasticity 12 6
7 Elasticity and regression analysis Even with few data points, an elasticity can in principle be estimated using a simple linear ( OLS ) regression model of the form: 1 2 where Y is the dependent variable (log of revenues), X is the explanatory variable (log of proxy tax base), and ε is an error term. We use logarithms because the estimate of a 2 is the estimated elasticity. We will have n values for Y and X, one for each observation in our estimation period. 13 Illustration: tax revenues vs. base (in logarithms) (MonteCarlo simulation) ln of revenue y = x R² = ln of base Using logs, the estimated elasticity is the slope of the regression model. Even though data were generated with a model exhibiting unit elasticity as the truth, the estimated elasticity is
8 Regression analysis The pattern of deviations (residuals) around this fitted line indicates how good a fit we have. The larger they are, the less our model is able to explain the evolution of Y by variations in X. If we have the forecast values for X, we can use the model to forecast values for Y. Because the model is imperfect, there will be errors around the forecast, which will depend on the distribution of the residuals. 15 Illustration: tax revenues vs. base (in log) (MonteCarlo simulation) 0.1 OLS residuals (of loglog model) These OLS residuals are very well behaved: the estimator of the elasticity is unbiased and efficient, even though it is WRONG. That was expected: underlying errors were generated randomly, assuming a normal distribution. But why is OLS estimator different from the truth? 16 8
9 Illustration: tax revenues vs. base (in log) (MonteCarlo simulation) 3 True errors (in $bn) Even though they were randomly generated (true!), this particular draw of error terms is such that there seems to be an (unintended) trend. This trend will be captured by the OLS estimation and explains why the estimated coefficient higher than the true model (1.2 > 1) there is always a confidence interval around the estimated elasticity. 17 Risks with Simple Estimation Our simple regression may yield good results because tax revenues and the tax base are both increasing. In technical language, we are dealing with nonstationary series. To be sure of our relationship, we need to use stationary series, meaning that there is no systematic tendency for the data to rise or fall over time. 9
10 Developing Stationary Series One way to solve the problem is to estimate an equation using the change in the log of revenues (rather than the log of revenues) and the change in the log of the tax base (rather than the log of the tax base). This usually provides stationary series. Another approach is to use cointegration analysis. Econometric software offers ways to do this. IMF course on Macroeconomic Forecasting teaches how to test for stationarity and do cointegration. What If You Can t Do Cointegration? Cointegration approach: combines longterm relationship with shortterm and estimates adjustment dynamics from ST to LT. Hard to do in data constrained environments. Second best: Focus the econometrics on shortterm relationship: we deliberately ignore the longterm and the implied dynamics. But at least, the trends will not pollute the simple regression estimation. For outer years of projections: assume convergence of coefficient towards an intuitive longterm value. Beware of results if using actual rather than adjusted data: will estimate buoyancy rather than elasticity if tax law or administration have changed noticeably during the period 20 10
11 Conclusion on estimation Simple model linking revenues to the tax base can be useful. Elasticity (buoyancy) can be estimated simply. But: Keep in mind presumed longterm value for elasticity (ideally around 1). The estimated elasticity will not necessarily be the true one! If data are actuals, estimate may be a buoyancy 21 III. From Projection to Forecast Use estimated elasticity cautiously. Does the overall value make sense? Large deviations from 1 must be substantiated. Compare with past realizations (point elasticities); Look for evidence of an emerging break in the estimated model (e.g. systematically positive or negative forecast errors over the last few years). Always plot data on charts, check residuals. Revenue Forecast: projection + adjustments f Rt 1 Rt 1 g elasticity Adjustments base 22 11
12 Adjustment factors Adjustments factors form the art dimension of forecasting. As it involves judgment, transparency is essential for the credibility of the forecast. The most common reasons for adjusting mechanical projections are: Temporary shocks have occurred in the past: base effect must be corrected (otherwise implicit assumption that the shock is permanent). Role of nonquantifiable/qualitative lit information about impending shocks. Assumption about compliance/enforcement/tax administration reforms must be clearly spelled out. Systematic revenue increases (decreases) during the period will bias estimated elasticity up (down) 23 Shortterm term and longer term Shortterm nature of the econometric relationship during a time of economic transition: ii Likelihood of unstable relationship (the past may not be a good predictor of the future) Be explicit about how you see longterm trends for outeryear (t+3 and beyond): Historical averages? Other assumptions? 24 12
13 When to Use Elasticity Approach Elasticity approach can be valuable when data suggest a nonlinear response of revenue to the proxy tax base: elasticity different from 1 If estimated elasticity equals 1, result is same as effective tax rate approach Risk arises if buoyancies or elasticities vary a lot from year to year. If so, using estimated elasticity may give poor forecast to revenue. Example: if tax base rises but revenue falls, buoyancy is negative. Is decline due to policy change? Can impact be estimated and data adjusted to show elasticity? Summary and Conclusion Elasticity approach allows revenues to grow faster or more slowly than the tax base Compare buoyancy and elasticity: Buoyancy is relationship between changes in actual revenues and changes in proxy tax base Elasticity reflects automatic change in revenues from change in tax base; represents an average response Buoyancies and elasticities can be estimated using regression approaches; note risks Beware of frequent yeartoyear changes in buoyancies or elasticities 13
Fiscal Analysis and Forecasting Workshop Bangkok, Thailand June 16 27, Joshua Greene
Revenue Fundamentals, Fiscal Forecasting, and the Effective Tax Rate Approach Fiscal Analysis and Forecasting Workshop Bangkok, Thailand June 16 27, 2014 Joshua Greene Consultant IMFTAOLAM training activities
More information4. Simple regression. QBUS6840 Predictive Analytics. https://www.otexts.org/fpp/4
4. Simple regression QBUS6840 Predictive Analytics https://www.otexts.org/fpp/4 Outline The simple linear model Least squares estimation Forecasting with regression Nonlinear functional forms Regression
More informationIntegrated Resource Plan
Integrated Resource Plan March 19, 2004 PREPARED FOR KAUA I ISLAND UTILITY COOPERATIVE LCG Consulting 4962 El Camino Real, Suite 112 Los Altos, CA 94022 6509629670 1 IRP 1 ELECTRIC LOAD FORECASTING 1.1
More informationAn Introduction to Time Series Regression
An Introduction to Time Series Regression Henry Thompson Auburn University An economic model suggests examining the effect of exogenous x t on endogenous y t with an exogenous control variable z t. In
More informationFORECASTING DEPOSIT GROWTH: Forecasting BIF and SAIF Assessable and Insured Deposits
Technical Paper Series Congressional Budget Office Washington, DC FORECASTING DEPOSIT GROWTH: Forecasting BIF and SAIF Assessable and Insured Deposits Albert D. Metz Microeconomic and Financial Studies
More informationThe Elasticity of Taxable Income: A NonTechnical Summary
The Elasticity of Taxable Income: A NonTechnical Summary John Creedy The University of Melbourne Abstract This paper provides a nontechnical summary of the concept of the elasticity of taxable income,
More informationA Primer on Forecasting Business Performance
A Primer on Forecasting Business Performance There are two common approaches to forecasting: qualitative and quantitative. Qualitative forecasting methods are important when historical data is not available.
More informationPITFALLS IN TIME SERIES ANALYSIS. Cliff Hurvich Stern School, NYU
PITFALLS IN TIME SERIES ANALYSIS Cliff Hurvich Stern School, NYU The t Test If x 1,..., x n are independent and identically distributed with mean 0, and n is not too small, then t = x 0 s n has a standard
More informationChapter 9. The ISLM/ADAS Model: A General Framework for Macroeconomic Analysis. 2008 Pearson AddisonWesley. All rights reserved
Chapter 9 The ISLM/ADAS Model: A General Framework for Macroeconomic Analysis Chapter Outline The FE Line: Equilibrium in the Labor Market The IS Curve: Equilibrium in the Goods Market The LM Curve:
More informationLecture 18 Linear Regression
Lecture 18 Statistics Unit Andrew Nunekpeku / Charles Jackson Fall 2011 Outline 1 1 Situation  used to model quantitative dependent variable using linear function of quantitative predictor(s). Situation
More informationChapter 5: Bivariate Cointegration Analysis
Chapter 5: Bivariate Cointegration Analysis 1 Contents: Lehrstuhl für Department Empirische of Wirtschaftsforschung Empirical Research and und Econometrics Ökonometrie V. Bivariate Cointegration Analysis...
More informationIs the Forward Exchange Rate a Useful Indicator of the Future Exchange Rate?
Is the Forward Exchange Rate a Useful Indicator of the Future Exchange Rate? Emily Polito, Trinity College In the past two decades, there have been many empirical studies both in support of and opposing
More informationMACROECONOMIC ANALYSIS OF VARIOUS PROPOSALS TO PROVIDE $500 BILLION IN TAX RELIEF
MACROECONOMIC ANALYSIS OF VARIOUS PROPOSALS TO PROVIDE $500 BILLION IN TAX RELIEF Prepared by the Staff of the JOINT COMMITTEE ON TAXATION March 1, 2005 JCX405 CONTENTS INTRODUCTION... 1 EXECUTIVE SUMMARY...
More informationThe VAR models discussed so fare are appropriate for modeling I(0) data, like asset returns or growth rates of macroeconomic time series.
Cointegration The VAR models discussed so fare are appropriate for modeling I(0) data, like asset returns or growth rates of macroeconomic time series. Economic theory, however, often implies equilibrium
More informationNot Your Dad s Magic Eight Ball
Not Your Dad s Magic Eight Ball Prepared for the NCSL Fiscal Analysts Seminar, October 21, 2014 Jim Landers, Office of Fiscal and Management Analysis, Indiana Legislative Services Agency Actual Forecast
More informationForecasting in supply chains
1 Forecasting in supply chains Role of demand forecasting Effective transportation system or supply chain design is predicated on the availability of accurate inputs to the modeling process. One of the
More informationCHAPTER 11. AN OVEVIEW OF THE BANK OF ENGLAND QUARTERLY MODEL OF THE (BEQM)
1 CHAPTER 11. AN OVEVIEW OF THE BANK OF ENGLAND QUARTERLY MODEL OF THE (BEQM) This model is the main tool in the suite of models employed by the staff and the Monetary Policy Committee (MPC) in the construction
More informationDEPARTMENT OF ECONOMICS. Unit ECON 12122 Introduction to Econometrics. Notes 4 2. R and F tests
DEPARTMENT OF ECONOMICS Unit ECON 11 Introduction to Econometrics Notes 4 R and F tests These notes provide a summary of the lectures. They are not a complete account of the unit material. You should also
More informationThe information content of lagged equity and bond yields
Economics Letters 68 (2000) 179 184 www.elsevier.com/ locate/ econbase The information content of lagged equity and bond yields Richard D.F. Harris *, Rene SanchezValle School of Business and Economics,
More informationSection A. Index. Section A. Planning, Budgeting and Forecasting Section A.2 Forecasting techniques... 1. Page 1 of 11. EduPristine CMA  Part I
Index Section A. Planning, Budgeting and Forecasting Section A.2 Forecasting techniques... 1 EduPristine CMA  Part I Page 1 of 11 Section A. Planning, Budgeting and Forecasting Section A.2 Forecasting
More informationChapter 9: Univariate Time Series Analysis
Chapter 9: Univariate Time Series Analysis In the last chapter we discussed models with only lags of explanatory variables. These can be misleading if: 1. The dependent variable Y t depends on lags of
More informationHow Much Equity Does the Government Hold?
How Much Equity Does the Government Hold? Alan J. Auerbach University of California, Berkeley and NBER January 2004 This paper was presented at the 2004 Meetings of the American Economic Association. I
More informationA Trading Strategy Based on the LeadLag Relationship of Spot and Futures Prices of the S&P 500
A Trading Strategy Based on the LeadLag Relationship of Spot and Futures Prices of the S&P 500 FE8827 Quantitative Trading Strategies 2010/11 MiniTerm 5 Nanyang Technological University Submitted By:
More information5 Comparison with the Previous Convergence Programme and Sensitivity Analysis
5 Comparison with the Previous Convergence Programme and Sensitivity Analysis 5.1 Comparison with the Previous Macroeconomic Scenario The differences between the macroeconomic scenarios of the current
More informationA MONETARIST MONEY DEMAND: FUNCTION
A MONETARIST MONEY DEMAND: FUNCTION Robert L. Hetzel Introduction In the first part of this article, inflation as a monetary phenomenon is discussed. The discussion is from the perspective of the modern
More informationChapter 7: Simple linear regression Learning Objectives
Chapter 7: Simple linear regression Learning Objectives Reading: Section 7.1 of OpenIntro Statistics Video: Correlation vs. causation, YouTube (2:19) Video: Intro to Linear Regression, YouTube (5:18) 
More informationMacroeconomic Analysis Econ 6022 Level I
1 / 66 Macroeconomic Analysis Econ 6022 Level I Lecture 8 Fall, 2011 2 / 66 Business Cycle Analysis: A Preview What explains business cycle fluctuations? Two major business cycle theories  Classical theory
More informationPredictability of Average Inflation over Long Time Horizons
Predictability of Average Inflation over Long Time Horizons Allan Crawford, Research Department Uncertainty about the level of future inflation adversely affects the economy because it distorts savings
More informationAn Evaluation of the Possible
An Evaluation of the Possible Macroeconomic Impact of the Income Tax Reduction in Malta Article published in the Quarterly Review 2015:2, pp. 4147 BOX 4: AN EVALUATION OF THE POSSIBLE MACROECONOMIC IMPACT
More informationChapter 25. Rational Expectations: Implications for Policy The Lucas Critique of Policy Evaluation
Chapter 25 Rational Expectations: Implications for Policy 25.1 The Lucas Critique of Policy Evaluation 1) Whether one views the activist policies of the 1960s and 1970s as destabilizing or believes the
More informationConditional guidance as a response to supply uncertainty
1 Conditional guidance as a response to supply uncertainty Appendix to the speech given by Ben Broadbent, External Member of the Monetary Policy Committee, Bank of England At the London Business School,
More informationRob J Hyndman. Forecasting using. 11. Dynamic regression OTexts.com/fpp/9/1/ Forecasting using R 1
Rob J Hyndman Forecasting using 11. Dynamic regression OTexts.com/fpp/9/1/ Forecasting using R 1 Outline 1 Regression with ARIMA errors 2 Example: Japanese cars 3 Using Fourier terms for seasonality 4
More informationMitchell H. Holt Dec 2008 Senior Thesis
Mitchell H. Holt Dec 2008 Senior Thesis Default Loans All lending institutions experience losses from default loans They must take steps to minimize their losses Only lend to low risk individuals Low Risk
More informationEconometric Modelling for Revenue Projections
Econometric Modelling for Revenue Projections Annex E 1. An econometric modelling exercise has been undertaken to calibrate the quantitative relationship between the five major items of government revenue
More informationLean Six Sigma Analyze Phase Introduction. TECH 50800 QUALITY and PRODUCTIVITY in INDUSTRY and TECHNOLOGY
TECH 50800 QUALITY and PRODUCTIVITY in INDUSTRY and TECHNOLOGY Before we begin: Turn on the sound on your computer. There is audio to accompany this presentation. Audio will accompany most of the online
More informationChapter 1. Vector autoregressions. 1.1 VARs and the identi cation problem
Chapter Vector autoregressions We begin by taking a look at the data of macroeconomics. A way to summarize the dynamics of macroeconomic data is to make use of vector autoregressions. VAR models have become
More informationMaximum Likelihood Estimation of an ARMA(p,q) Model
Maximum Likelihood Estimation of an ARMA(p,q) Model Constantino Hevia The World Bank. DECRG. October 8 This note describes the Matlab function arma_mle.m that computes the maximum likelihood estimates
More informationAge to Age Factor Selection under Changing Development Chris G. Gross, ACAS, MAAA
Age to Age Factor Selection under Changing Development Chris G. Gross, ACAS, MAAA Introduction A common question faced by many actuaries when selecting loss development factors is whether to base the selected
More informationEmployment, unemployment and real economic growth. Ivan Kitov Institute for the Dynamics of the Geopsheres, Russian Academy of Sciences
Employment, unemployment and real economic growth Ivan Kitov Institute for the Dynamics of the Geopsheres, Russian Academy of Sciences Oleg Kitov Department of Economics, University of Oxford Abstract
More informationModule 5: Multiple Regression Analysis
Using Statistical Data Using to Make Statistical Decisions: Data Multiple to Make Regression Decisions Analysis Page 1 Module 5: Multiple Regression Analysis Tom Ilvento, University of Delaware, College
More information16 : Demand Forecasting
16 : Demand Forecasting 1 Session Outline Demand Forecasting Subjective methods can be used only when past data is not available. When past data is available, it is advisable that firms should use statistical
More informationSHORT TERM EFFECTS OF MONEY INFLATION AND UNEMPLOYMENT THE NEOCLASSICAL SYNTHESIS
SHORT TERM EFFECTS OF MONEY INFLATION AND UNEMPLOYMENT THE NEOCLASSICAL SYNTHESIS Prices increase with excess nominal aggregate demand π(t) = p(t)  p(t1) = k[yd(t) ys(t)] = h u(t) k > 0, h < 0 The Phillips
More informationNonlinear Regression Functions. SW Ch 8 1/54/
Nonlinear Regression Functions SW Ch 8 1/54/ The TestScore STR relation looks linear (maybe) SW Ch 8 2/54/ But the TestScore Income relation looks nonlinear... SW Ch 8 3/54/ Nonlinear Regression General
More informationChapter 6. Econometrics. 6.1 Introduction. 6.2 Univariate techniques Transforming data
Chapter 6 Econometrics 6.1 Introduction We re going to use a few tools to characterize the time series properties of macro variables. Today, we will take a relatively atheoretical approach to this task,
More informationInequality, Mobility and Income Distribution Comparisons
Fiscal Studies (1997) vol. 18, no. 3, pp. 93 30 Inequality, Mobility and Income Distribution Comparisons JOHN CREEDY * Abstract his paper examines the relationship between the crosssectional and lifetime
More informationProblems with OLS Considering :
Problems with OLS Considering : we assume Y i X i u i E u i 0 E u i or var u i E u i u j 0orcov u i,u j 0 We have seen that we have to make very specific assumptions about u i in order to get OLS estimates
More informationA Short review of steel demand forecasting methods
A Short review of steel demand forecasting methods Fujio John M. Tanaka This paper undertakes the present and past review of steel demand forecasting to study what methods should be used in any future
More informationDividendPrice Ratios and Stock Returns: Another Look at the History
First draft: January 2012 Current version: March 2012 DividendPrice Ratios and Stock Returns: Another Look at the History BRADFORD CORNELL CALIFORNIA INSTITUTE OF TECHNOLOGY PASADENA, CA 91125 626 5642001
More informationRelationship among crude oil prices, share prices and exchange rates
Relationship among crude oil prices, share prices and exchange rates Do higher share prices and weaker dollar lead to higher crude oil prices? Akira YANAGISAWA Leader Energy Demand, Supply and Forecast
More informationVI. Real Business Cycles Models
VI. Real Business Cycles Models Introduction Business cycle research studies the causes and consequences of the recurrent expansions and contractions in aggregate economic activity that occur in most industrialized
More information2. Linear regression with multiple regressors
2. Linear regression with multiple regressors Aim of this section: Introduction of the multiple regression model OLS estimation in multiple regression Measuresoffit in multiple regression Assumptions
More informationNCSS Statistical Software Principal Components Regression. In ordinary least squares, the regression coefficients are estimated using the formula ( )
Chapter 340 Principal Components Regression Introduction is a technique for analyzing multiple regression data that suffer from multicollinearity. When multicollinearity occurs, least squares estimates
More informationChapter 9 The ISLM/ADAS Model: A General Framework for Macroeconomic Analysis
Chapter 9 The ISLM/ADAS Model: A General Framework for Macroeconomic Analysis Multiple Choice Questions 1. The FE line shows the level of output at which the market is in equilibrium. (a) Goods (b) Asset
More informationOLS is not only unbiased it is also the most precise (efficient) unbiased estimation technique  ie the estimator has the smallest variance
Lecture 5: Hypothesis Testing What we know now: OLS is not only unbiased it is also the most precise (efficient) unbiased estimation technique  ie the estimator has the smallest variance (if the GaussMarkov
More informationADVANCED FORECASTING MODELS USING SAS SOFTWARE
ADVANCED FORECASTING MODELS USING SAS SOFTWARE Girish Kumar Jha IARI, Pusa, New Delhi 110 012 gjha_eco@iari.res.in 1. Transfer Function Model Univariate ARIMA models are useful for analysis and forecasting
More informationManual on Air Traffic Forecasting
Doc 8991 AT/722/3 Manual on Air Traffic Forecasting Approved by the Secretary General and published under his authority Third Edition 2006 International Civil Aviation Organization AMENDMENTS The issue
More informationMarketing Mix Modelling and Big Data P. M Cain
1) Introduction Marketing Mix Modelling and Big Data P. M Cain Big data is generally defined in terms of the volume and variety of structured and unstructured information. Whereas structured data is stored
More information, then the form of the model is given by: which comprises a deterministic component involving the three regression coefficients (
Multiple regression Introduction Multiple regression is a logical extension of the principles of simple linear regression to situations in which there are several predictor variables. For instance if we
More informationNonStationary Time Series, Cointegration and Spurious Regression
Econometrics 2 Fall 25 NonStationary Time Series, Cointegration and Spurious Regression Heino Bohn Nielsen 1of32 Motivation: Regression with NonStationarity What happens to the properties of OLS if variables
More informationSELFTEST: SIMPLE REGRESSION
ECO 22000 McRAE SELFTEST: SIMPLE REGRESSION Note: Those questions indicated with an (N) are unlikely to appear in this form on an inclass examination, but you should be able to describe the procedures
More informationX X X a) perfect linear correlation b) no correlation c) positive correlation (r = 1) (r = 0) (0 < r < 1)
CORRELATION AND REGRESSION / 47 CHAPTER EIGHT CORRELATION AND REGRESSION Correlation and regression are statistical methods that are commonly used in the medical literature to compare two or more variables.
More informationCauses of Inflation in the Iranian Economy
Causes of Inflation in the Iranian Economy Hamed Armesh* and Abas Alavi Rad** It is clear that in the nearly last four decades inflation is one of the important problems of Iranian economy. In this study,
More informationStatistics in Retail Finance. Chapter 6: Behavioural models
Statistics in Retail Finance 1 Overview > So far we have focussed mainly on application scorecards. In this chapter we shall look at behavioural models. We shall cover the following topics: Behavioural
More information( ) Chapter 14. Questions for Review. 1. The equation for the dynamic aggregatesupply curve is:! t =! t"1 +# (Y t " Y t ) + $ t.
Chapter 14 Questions for Review 1. The equation for the dynamic aggregatesupply curve is:! t =! t"1 +# Y t " Y t ) + $ t. Recall that ϕ is a positive parameter that measures how firms adjust their prices
More informationMassachusetts Department of Revenue. Briefing Book FY2015 Consensus Revenue Estimate Hearing. December 11, 2013. Presented by: Amy Pitter COMMISSIONER
Massachusetts Department of Revenue Briefing Book FY2015 Consensus Revenue Estimate Hearing December 11, 2013 Presented by: Amy Pitter COMMISSIONER Kazim P. Ozyurt DIRECTOR OFFICE OF TAX POLICY ANALYSIS
More informationAnalysis of Bayesian Dynamic Linear Models
Analysis of Bayesian Dynamic Linear Models Emily M. Casleton December 17, 2010 1 Introduction The main purpose of this project is to explore the Bayesian analysis of Dynamic Linear Models (DLMs). The main
More informationSimple linear regression
Simple linear regression Introduction Simple linear regression is a statistical method for obtaining a formula to predict values of one variable from another where there is a causal relationship between
More informationWooldridge, Introductory Econometrics, 4th ed. Multiple regression analysis:
Wooldridge, Introductory Econometrics, 4th ed. Chapter 4: Inference Multiple regression analysis: We have discussed the conditions under which OLS estimators are unbiased, and derived the variances of
More informationChapter 12. Unemployment and Inflation. 2008 Pearson AddisonWesley. All rights reserved
Chapter 12 Unemployment and Inflation Chapter Outline Unemployment and Inflation: Is There a TradeOff? The Problem of Unemployment The Problem of Inflation 122 Unemployment and Inflation: Is There a
More informationExample: Credit card default, we may be more interested in predicting the probabilty of a default than classifying individuals as default or not.
Statistical Learning: Chapter 4 Classification 4.1 Introduction Supervised learning with a categorical (Qualitative) response Notation:  Feature vector X,  qualitative response Y, taking values in C
More informationCorporate Defaults and Large Macroeconomic Shocks
Corporate Defaults and Large Macroeconomic Shocks Mathias Drehmann Bank of England Andrew Patton London School of Economics and Bank of England Steffen Sorensen Bank of England The presentation expresses
More informationThe Response of Stock Prices to Permanent and Temporary Shocks to Dividends. Author: BongSoo Lee Presenter: Omar Salomon
The Response of Stock Prices to Permanent and Temporary Shocks to Dividends Author: BongSoo Lee Presenter: Omar Salomon AGENDA 1 2 3 4 5 Abstract Introduction Model Development Empirical Results Conclusions
More informationOutline: Demand Forecasting
Outline: Demand Forecasting Given the limited background from the surveys and that Chapter 7 in the book is complex, we will cover less material. The role of forecasting in the chain Characteristics of
More informationCalculation of Medical Liability  Combination of Statistical Methods, Actuarial Judgment, and Communication
Calculation of Medical Liability  Combination of Statistical Methods, Actuarial Judgment, and Communication Jed Linfield, FSA, MAAA AmeriChoice/UnitedHealth Care Southeastern Actuaries Conference Atlanta,
More informationThe Multiple Regression Model: Hypothesis Tests and the Use of Nonsample Information
Chapter 8 The Multiple Regression Model: Hypothesis Tests and the Use of Nonsample Information An important new development that we encounter in this chapter is using the F distribution to simultaneously
More informationC: LEVEL 800 {MASTERS OF ECONOMICS( ECONOMETRICS)}
C: LEVEL 800 {MASTERS OF ECONOMICS( ECONOMETRICS)} 1. EES 800: Econometrics I Simple linear regression and correlation analysis. Specification and estimation of a regression model. Interpretation of regression
More informationCHAPTER 5. Exercise Solutions
CHAPTER 5 Exercise Solutions 91 Chapter 5, Exercise Solutions, Principles of Econometrics, e 9 EXERCISE 5.1 (a) y = 1, x =, x = x * * i x i 1 1 1 1 1 1 1 1 1 1 1 1 1 1 y * i (b) (c) yx = 1, x = 16, yx
More information5. Multiple regression
5. Multiple regression QBUS6840 Predictive Analytics https://www.otexts.org/fpp/5 QBUS6840 Predictive Analytics 5. Multiple regression 2/39 Outline Introduction to multiple linear regression Some useful
More informationRevenue Administration: Performance Measurement in Tax Administration
T e c h n i c a l N o t e s a n d M a n u a l s Revenue Administration: Performance Measurement in Tax Administration William Crandall Fiscal Affairs Department I n t e r n a t i o n a l M o n e t a r
More informationElements of statistics (MATH04871)
Elements of statistics (MATH04871) Prof. Dr. Dr. K. Van Steen University of Liège, Belgium December 10, 2012 Introduction to Statistics Basic Probability Revisited Sampling Exploratory Data Analysis 
More informationSimultaneous Equation Models As discussed last week, one important form of endogeneity is simultaneity. This arises when one or more of the
Simultaneous Equation Models As discussed last week, one important form of endogeneity is simultaneity. This arises when one or more of the explanatory variables is jointly determined with the dependent
More informationSimple Linear Regression Inference
Simple Linear Regression Inference 1 Inference requirements The Normality assumption of the stochastic term e is needed for inference even if it is not a OLS requirement. Therefore we have: Interpretation
More informationNow or Later? Wind Power Surpluses, Shortfalls and Trading on Short Term Markets
Now or Later? Wind Power Surpluses, Shortfalls and Trading on Short Term Markets Johannes Mauritzen Research Institute of Industrial Economics (IFN) Stockholm, Sweden jmaurit@gmail.com Abstract Organizing
More informationFEV1 (litres) Figure 1: Models for gas consumption and lung capacity
Simple Linear Regression: Reliability of predictions Richard Buxton. 2008. 1 Introduction We often use regression models to make predictions. In Figure 1 (a), we ve fitted a model relating a household
More information12.1 Introduction. 12.2 The MP Curve: Monetary Policy and the Interest Rates 1/24/2013. Monetary Policy and the Phillips Curve
Chapter 12 Monetary Policy and the Phillips Curve By Charles I. Jones Media Slides Created By Dave Brown Penn State University The shortrun model summary: Through the MP curve the nominal interest rate
More informationSYSTEMS OF REGRESSION EQUATIONS
SYSTEMS OF REGRESSION EQUATIONS 1. MULTIPLE EQUATIONS y nt = x nt n + u nt, n = 1,...,N, t = 1,...,T, x nt is 1 k, and n is k 1. This is a version of the standard regression model where the observations
More informationPrediction and Confidence Intervals in Regression
Fall Semester, 2001 Statistics 621 Lecture 3 Robert Stine 1 Prediction and Confidence Intervals in Regression Preliminaries Teaching assistants See them in Room 3009 SHDH. Hours are detailed in the syllabus.
More informationTime series Forecasting using HoltWinters Exponential Smoothing
Time series Forecasting using HoltWinters Exponential Smoothing Prajakta S. Kalekar(04329008) Kanwal Rekhi School of Information Technology Under the guidance of Prof. Bernard December 6, 2004 Abstract
More informationSensex Realized Volatility Index
Sensex Realized Volatility Index Introduction: Volatility modelling has traditionally relied on complex econometric procedures in order to accommodate the inherent latent character of volatility. Realized
More informationChapter 27 Using Predictor Variables. Chapter Table of Contents
Chapter 27 Using Predictor Variables Chapter Table of Contents LINEAR TREND...1329 TIME TREND CURVES...1330 REGRESSORS...1332 ADJUSTMENTS...1334 DYNAMIC REGRESSOR...1335 INTERVENTIONS...1339 TheInterventionSpecificationWindow...1339
More informationModels for Product Demand Forecasting with the Use of Judgmental Adjustments to Statistical Forecasts
Page 1 of 20 ISF 2008 Models for Product Demand Forecasting with the Use of Judgmental Adjustments to Statistical Forecasts Andrey Davydenko, Professor Robert Fildes a.davydenko@lancaster.ac.uk Lancaster
More informationIntroduction to Dynamic Models. Slide set #1 (Ch 1.11.6 in IDM).
1 Introduction Introduction to Dynamic Models. Slide set #1 (Ch 1.11.6 in IDM). Ragnar Nymoen University of Oslo, Department of Economics We observe that economic agents take time to adjust their behaviour
More informationAP Statistics. Chapter 4 Review
Name AP Statistics Chapter 4 Review 1. In a study of the link between high blood pressure and cardiovascular disease, a group of white males aged 35 to 64 was followed for 5 years. At the beginning of
More informationbusiness statistics using Excel OXFORD UNIVERSITY PRESS Glyn Davis & Branko Pecar
business statistics using Excel Glyn Davis & Branko Pecar OXFORD UNIVERSITY PRESS Detailed contents Introduction to Microsoft Excel 2003 Overview Learning Objectives 1.1 Introduction to Microsoft Excel
More informationSCOTLAND S FISCAL FRAMEWORK WRITTEN SUBMISSION FROM PROFESSOR DAVID BELL. 1. Introduction... 1. 2. Forecasting... 1. 3. Data... 4
SCOTLAND S FISCAL FRAMEWORK WRITTEN SUBMISSION FROM PROFESSOR DAVID BELL Contents 1. Introduction... 1 2. Forecasting... 1 3. Data... 4 4. Reporting by the Independent Fiscal Body... 5 5. Revenue Maximisation...
More information2013 MBA Jump Start Program. Statistics Module Part 3
2013 MBA Jump Start Program Module 1: Statistics Thomas Gilbert Part 3 Statistics Module Part 3 Hypothesis Testing (Inference) Regressions 2 1 Making an Investment Decision A researcher in your firm just
More informationDemand forecasting & Aggregate planning in a Supply chain. Session Speaker Prof.P.S.Satish
Demand forecasting & Aggregate planning in a Supply chain Session Speaker Prof.P.S.Satish 1 Introduction PEMPEMM2506 Forecasting provides an estimate of future demand Factors that influence demand and
More informationRegression Analysis Using ArcMap. By Jennie Murack
Regression Analysis Using ArcMap By Jennie Murack Regression Basics How is Regression Different from other Spatial Statistical Analyses? With other tools you ask WHERE something is happening? Are there
More informationExploring the IntraMetropolitan Dynamics of the London Office Market
Exploring the IntraMetropolitan Dynamics of the London Office Market Paper Presented at the PacificRim Real Estate Society Annual Conference, Auckland, New Zealand, January 2006 Simon Stevenson, Cass
More informationThe importance of graphing the data: Anscombe s regression examples
The importance of graphing the data: Anscombe s regression examples Bruce Weaver Northern Health Research Conference Nipissing University, North Bay May 3031, 2008 B. Weaver, NHRC 2008 1 The Objective
More information